【Luogu】P4172水管局长（LCT）

　　题目链接

　　有个结论是x到y的路径上最长边权值等于最小生成树上最长边权值，于是问题转化为最小生成树。

　　再考虑把问题反过来，删边变成加边。

　　于是变成动态维护最小生成树，LCT可以做到。

　　

#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<cctype>
#include<cstring>
#include<map>
#define maxn 200020
using namespace std;
inline long long read(){
    long long num=,f=;
    char ch=getchar();
    while(!isdigit(ch)){
        if(ch=='-')    f=-;
        ch=getchar();
    }
    while(isdigit(ch)){
        num=num*+ch-'';
        ch=getchar();
    }
    return num*f;
}

struct Edge{
    int from,to,val;
    bool operator <(const Edge &a)const{    return val<a.val;    }
}edge[maxn];

int stack[maxn],top;

struct Splay{
    struct Node{
        int e[],fa,mini,tag,val,maxi;
    }tree[maxn];
    inline int iden(int x){    return x==tree[tree[x].fa].e[];    }
    inline void connect(int x,int fa,int how){    tree[x].fa=fa;    tree[fa].e[how]=x;    }
    inline bool isroot(int x){    return tree[tree[x].fa].e[]!=x&&tree[tree[x].fa].e[]!=x;    }
    inline void update(int x){
        int le=tree[x].e[],ri=tree[x].e[];    tree[x].maxi=tree[x].val;
        if(edge[tree[le].maxi].val>edge[tree[x].maxi].val)    tree[x].maxi=tree[le].maxi;
        if(edge[tree[ri].maxi].val>edge[tree[x].maxi].val)    tree[x].maxi=tree[ri].maxi;
    }
    inline void reverse(int x){
        swap(tree[x].e[],tree[x].e[]);
        tree[x].tag^=;
    }
    inline void pushdown(int x){
        if(tree[x].tag==)    return;
        if(tree[x].e[])    reverse(tree[x].e[]);
        if(tree[x].e[])    reverse(tree[x].e[]);
        tree[x].tag=;
    }
    void rotate(int x){
        int y=tree[x].fa,r=tree[y].fa;
        int sony=iden(x),sonr=iden(y);
        tree[x].fa=r;    if(!isroot(y))    tree[r].e[sonr]=x;
        int b=tree[x].e[sony^];
        connect(b,y,sony);
        connect(y,x,sony^);
        update(y);
    }
    inline void pushto(int x){
        top=;
        while(!isroot(x)){
            stack[++top]=x;
            x=tree[x].fa;
        }
        pushdown(x);
        while(top)    pushdown(stack[top--]);
    }
    void splay(int x){
        pushto(x);
        while(!isroot(x)){
            int fa=tree[x].fa;
            if(!isroot(fa))
                if(iden(fa)==iden(x))    rotate(fa);
                else                    rotate(x);
            rotate(x);
        }
        update(x);
    }
    inline void access(int x){
        int last=;
        while(x){
            splay(x);
            tree[x].e[]=last;
            update(x);
            last=x;    x=tree[x].fa;
        }
    }
    inline void makeroot(int x){
        access(x);
        splay(x);
        reverse(x);
    }
    inline int findroot(int x){
        access(x);
        splay(x);
        while(tree[x].e[])    x=tree[x].e[];
        return x;
    }
    inline void split(int x,int y){
        makeroot(x);
        access(y);
        splay(y);
    }
    inline void link(int x,int y){
        //printf("%d %d\n",x,y);
        split(x,y);
        tree[x].fa=y;
    }
    inline void cut(int x,int y){
        //printf("%d %d\n",x,y);
        split(x,y);
        if(tree[y].e[]!=x||tree[x].e[])    return;
        tree[x].fa=tree[y].e[]=;
    }
}s;

struct Que{
    int opt,x,y,id,cnt;
}q[maxn];
int cnt;

int ans[maxn];

int d[maxn*];

bool vis[maxn];

int main(){
    int n=read(),m=read(),e=read();
    for(int i=;i<=m;++i){
        edge[i]=(Edge){read(),read(),read()};
        if(edge[i].from>edge[i].to)    swap(edge[i].from,edge[i].to);
    }
    sort(edge+,edge+m+);
    for(int i=;i<=m;++i){
        //printf("%d %d>><\n",edge[i].from,edge[i].to);
        s.tree[i+n].mini=s.tree[i+n].val=i;
        d[edge[i].from*n+edge[i].to]=i;
    }
    for(int i=;i<=e;++i){
        q[i]=(Que){read(),read(),read(),};
        if(q[i].x>q[i].y)    swap(q[i].x,q[i].y);
        if(q[i].opt==)    q[i].id=++cnt;
        else{
            int now=d[q[i].x*n+q[i].y];
            q[i].cnt=now;
            //printf("%d\n",now);
            vis[now]=;
        }
    }
    int sum=;
    for(int i=;i<=m;++i){
        if(sum==n-)    break;
        if(vis[i])    continue;
        if(s.findroot(edge[i].from)==s.findroot(edge[i].to))    continue;
        s.link(edge[i].from,i+n);
        s.link(edge[i].to,i+n);
        sum++;
    }
    for(int i=e;i;--i){
        if(q[i].opt==){
            s.split(q[i].x,q[i].y);
            ans[q[i].id]=edge[s.tree[q[i].y].maxi].val;
        }
        else{
            s.split(q[i].x,q[i].y);
            int now=q[i].cnt;
            int ret=s.tree[q[i].y].maxi;
            if(edge[now].val<edge[ret].val){
                if(edge[ret].from)    s.cut(edge[ret].from,ret+n);
                if(edge[ret].to)    s.cut(edge[ret].to,ret+n);
                s.link(q[i].x,now+n);
                s.link(q[i].y,now+n);
            }
        }
    }
    for(int i=;i<=cnt;++i)    printf("%d\n",ans[i]);
    return ;
}